© 1992

Numerical Integration

Recent Developments, Software and Applications

  • Terje O. Espelid
  • Alan Genz

Part of the NATO ASI Series book series (ASIC, volume 357)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Numerical Integration Rules

  3. Numerical Integration Error Analysis

    1. Walter Gautschi
      Pages 133-145
    2. Ricolindo Cariño, Ian Robinson, Elise de Doncker
      Pages 175-186
  4. Numerical Integration Applications

About this book


This volume contains refereed papers and extended abstracts of papers presented at the NATO Advanced Research Workshop entitled 'Numerical Integration: Recent Develop­ ments, Software and Applications', held at the University of Bergen, Bergen, Norway, June 17-21,1991. The Workshop was attended by thirty-eight scientists. A total of eight NATO countries were represented. Eleven invited lectures and twenty-three contributed lectures were presented, of which twenty-five appear in full in this volume, together with three extended abstracts and one note. The main focus of the workshop was to survey recent progress in the theory of methods for the calculation of integrals and show how the theoretical results have been used in software development and in practical applications. The papers in this volume fall into four broad categories: numerical integration rules, numerical integration error analysis, numerical integration applications and numerical integration algorithms and software. It is five years since the last workshop of this nature was held, at Dalhousie University in Halifax, Canada, in 1986. Recent theoretical developments have mostly occurred in the area of integration rule construction. For polynomial integrating rules, invariant theory and ideal theory have been used to provide lower bounds on the numbers of points for different types of multidimensional rules, and to help in structuring the nonlinear systems which must be solved to determine the points and weights for the rules. Many new optimal or near optimal rules have been found for a variety of integration regions using these techniques.


Numerical integration STATISTICA algorithms cubature finite element method

Editors and affiliations

  • Terje O. Espelid
    • 1
  • Alan Genz
    • 2
  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.School of Electrical Engineering and Computer ScienceWashington State UniversityPullmanUSA

Bibliographic information

  • Book Title Numerical Integration
  • Book Subtitle Recent Developments, Software and Applications
  • Editors T.O. Espelid
    Alan Genz
  • Series Title NATO ASI Series
  • DOI
  • Copyright Information Kluwer Academic Publishers 1992
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-7923-1583-4
  • Softcover ISBN 978-94-010-5169-9
  • eBook ISBN 978-94-011-2646-5
  • Series ISSN 1389-2185
  • Edition Number 1
  • Number of Pages XII, 367
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Numeric Computing
    Computational Mathematics and Numerical Analysis
  • Buy this book on publisher's site
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